Permutation and combination practice · Mixed difficulty

If ${\;^{12}}{P_r} = 1320$, then $r$ is equal to

The number of ways in which the letters of the word BALLOON can be arranged so that two L's do not come together, is

At an election, a voter may vote for any number of candidates not greater than the number to be chosen. There are 10 candidates and 5 members to be selected. The number of ways of in which a voter can vote is:

The number of numbers that can be formed by using digits 1,2,3,4,3,2,1 so that odd digits always occupy odd places

The number of permutations of 4 letters from the letters of word 'KOLKATA' is

If ${\;^{n + 2}}{C_8}\;:{\;^{n - 2}}{P_4} = 57\;:16,$ then the value of $n$ is

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

The number of integers greater than 6000 that can be formed using the digits $3,5,6,7$ and 8 without repetition, is

Ashok, Usha, Rani, Sonu are to give speeches in a class. The teacher can arrange the order of their presentation in

The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is:

The value of $\frac{{ }^{20} C_n}{{ }^{25} C_m}$ when both numerator and denominator have their greatest values, is

The number of ways that 8 beads of different colours be strung as a necklace is

A class has 21 students. The class teacher has been asked to make $n$ groups of $r$ students each and go to zoo taking one group at a time. The size of group zoo i.e. the value of $r$) for which the teacher goes to the maximum number of times is (no group can go to the zoo twice)

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated, is

The number of 3 digit numbers ' $a b c$ ' such that $b < c$ is

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

The number of positive integers $< 1,00,000$ which contain exactly one 2, one 5 and one 7 in its decimal representation is

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is

Let $A = \left\{ {{x_1},{x_{2,}}{x_3},\;{x_4},\;{x_5},\;{x_6}} \right\}$,
$B = \left\{ {{y_1},\;{y_2},\;{y_3},{y_4},{y_5},{y_6}} \right\}.$ . Then the number of one – one mapping from $A$ to $B$ such that $f\left( {{x_i}} \right) \ne {y_v}i = 1,\;2,\;3,\;4,\;5,\;6$

The letters of the word RANDOM are written in all possible orders and these words are written out as in a dictionary, then the rank of the word RANDOM is

In a country, no two persons have identical set of teeth and there is no person without a tooth, also no person has more than 32 teeth. If shape and size of tooth is disregarded and only the position of tooth is considered, then maximum population of that country can be

The number of ways in which the letters of 'ARRANGE' be arranged so that i. "No two R's come together is